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Dom/deg: both dom+deg and dom+futdeg use the domain size as the main criterion. The degree of the variables is considered only in case of ties. Alternatively, Bessiere and Régin [BES 96] combined dom with deg in a new heuristic called dom/deg. The dom/deg does not give priority to the domain size or degree of variables but uses them equally. This heuristic selects the variable that minimizes the ratio of current domain size to static degree. Bessiere and Régin have been shown that dom/deg gives good results in comparison with dom when the constraint graphs are sparse but performs badly on dense constraint graphs.

Following the same principle of Haralick and Elliott saying that search efﬁciency is due to earlier failure, Smith and Grant [SMI 98] have derived from dom new heuristics that detect failures earlier than dom. Their study is based on an intuitive hypothesis saying that earlier detection of failure should lead the heuristic to lower search effort. Surprisingly, Smith and Grant’s experiments refuted this hypothesis contrary to their expectations. They concluded that increasing the ability to fail early in the search did not always lead to increase its efﬁciency.

Thus, only values having a support on D(xj ) are kept in D(xi ). The function Revise returns true if the domain of variable xi has been reduced, false otherwise (line 6). If Revise results in the removal of values from D(xi ), it can be the case that a value for another variable xk has lost its support on D(xi ). Thus, all ordered pairs (xk , xi ) such that k = j are added onto Q 3 Other data structures as queue or stack can perfectly serve the purpose. 22 Algorithms and Ordering Heuristics for DisCSPs so long as they are not already on Q in order to revise the domain of xk .